I agree with Karen. Nip it in the bud. Don't let her talk with you like that. So what if she thinks you are going to visit a GF? What is it her business now anyway? She LEFT YOU, remember?
It is not her business what you do. Although, IMHO, I would AVOID changing your schedule with the kids. That is unfair on the children, they are expecting to see Dad and they need stability in their life regarding you. If you are not there or if you are 'unreliable' they will suffer. So if you have arranged to see them certain times, you need to make that your #1 PRIORITY. Got it?
Now, outside of that, it's totally up to you what you do with your time. Nobody's business. No need to defend yourself. No need to explain to her your reasons. YOU DON'T OWE HER AN EXPLANATION. Don't give her more ammonition, Mark!
Me:39 H:40 S:9 D:7 First Bomb ONS:June 07 Second Bomb OW: March 08 Separated: March 08 M:15 yrs T:18 yrs H deep into A with OW Achieved ACCEPTANCE May 30, 09